Calculating Size of Star Image with Converging Lens

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Homework Help Overview

The discussion revolves around calculating the size of an image produced by a converging lens when observing a star, which is treated as a point source for optical purposes. The original poster presents a specific scenario involving a lens with given dimensions and asks for verification of their calculated image diameter using diffraction principles.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the validity of treating stars as point sources in optics, question the original poster's calculations, and discuss the implications of diffraction on image size. There are references to relevant optical principles and external resources for further clarification.

Discussion Status

The discussion is ongoing with participants providing insights and questioning the assumptions made about the nature of stars and their representation in optical systems. Some guidance has been offered through external links, but no consensus has been reached regarding the calculations or the assumptions about point sources.

Contextual Notes

Participants note the complexity of the problem due to the nature of stars and the distances involved, as well as the lack of information about the angle subtended by the star at Earth. There is also mention of potential mistakes in unit conversions affecting the calculations.

Emilyjoint
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An image of a point source (star) at infinity produces an image using a converging lens of diameter 50mm and focal length 500mm. Calculate the diameter of the resulting image.(take wavelengthof light to be 4x10^-7m)
I ask this because it is to do with seeing stars through a telescope.
I think the diameter is caclulated using diffraction principles to be 8mm Can anyone check to see if you get the same answer.
I used Sinθ = λ/a
 
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A star is not a point source.

A star is a ball.
 
Char. Limit said:
A star is not a point source.

A star is a ball.

That is essentially true, but because of the distances involved it can be regarded as a point source from an optical point of view

Dave
 
OK./...would a point source produce an image of this size?
 
Looked at that but could not see how it relates to a point source.
S it OK to use Sin theta = λ/a to calculate th width
 
Thanks for the help.Used the Calc site and got 9x10^-3mm...i had made a mistake with units.
got it now
 
Emilyjoint said:
OK./...would a point source produce an image of this size?

The size of image from a star is dependent on its relative magnitude (brightness) and the optics of your imaging system (diffraction and other aberrations). There is no clue about the angle subtended by it at the Earth.

(Most) planets in the Solar System subtend a big enough angle to distinguish the actual angular diameter of their disc (they look like little moons) but even the nearest star is a 'point' source to all intents and purposes.
 

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